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Journal Articles Applicable Analysis Year : 2009

On the existence of transmission eigenvalues in an inhomogeneous medium

Fioralba Cakoni
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Houssem Haddar

Abstract

We prove the existence of transmission eigenvalues corresponding to the inverse scattering problem for isotropic and anisotropic media for both the scalar problem and Maxwell's equations. Considering a generalized abstract eigenvalue problem, we are able to extend the ideas of Päivärinta and Sylvester [Transmission eigenvalues, SIAM J. Math. Anal. 40, (2008) pp. 783-753] to prove the existence of transmission eigenvalues for a larger class of interior transmission problems. Our analysis includes both the case of a medium with positive contrast and of a medium with negative contrast provided that the contrasts are large enough.

Dates and versions

hal-00743824 , version 1 (20-10-2012)

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Fioralba Cakoni, Houssem Haddar. On the existence of transmission eigenvalues in an inhomogeneous medium. Applicable Analysis, 2009, 88 (4), pp.475-493. ⟨10.1080/00036810802713966⟩. ⟨hal-00743824⟩
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